It was Holtby's fourth shutout of the season and second against the Jets. He also blanked Winnipeg 3-0 on March 2, the only times Winnipeg has been shut out this season.
Ondrej Pavelec faced 25 shots as the Jets (16-13-2) had their three-game home winning streak snapped.
Winnipeg stays in the Southeast Division's top spot and the third seed in the Eastern Conference, two points ahead of the Carolina Hurricanes, who lost 4-1 to New Jersey Thursday night.
The Jets and Washington face off again Friday night in Winnipeg.
The Jets were on their second power play early in the third, but Brooks Laich got control of the puck and was stopped on a breakaway by Pavelec.
Kane and Antti Miettinen challenged Holtby on a two-on-one midway through the period, but the netminder snapped out his right leg and stopped Miettinen's shot.
Pavelec took a delay of game penalty late in the third period and it proved costly.
With Olli Jokinen serving the penalty, Ovechkin scored his 13th goal of the season. Backstrom sent a pass to Ovechkin and he fired it high on Pavelec's glove side at 14:06.
It was then Ovechkin's turn to send a pass to Backstrom in the high slot and he put the puck between Pavelec and the post at 18:22 of the third.
Brouwer opened the game's scoring with a wrist shot from near the bottom of the faceoff circle that beat Pavelec at 3:06 of the first period, extending his points streak to three games (two goals, two assists).
Laich assisted on the goal for his first point of the season after making his season debut March 19 following a lengthy groin injury.
Jets forward Evander Kane had a good opportunity late in the period when he found himself alone in front of the net, but he couldn't get his stick on the puck to make a shot.
A couple minutes later, Ovechkin sent the puck past Winnipeg defenceman Dustin Byfuglien to Johannson, who redirected the puck into the net at 16:22 for the 2-0 lead.
Ovechkin put a couple of big hits on Winnipeg players in the second period, including defenceman Mark Stuart, who left the ice after the hit. He returned for one shift in the third, but left again for the dressing room.
The Jets outshot the Caps 4-3 in the second, but Washington kept a 13-12 edge in shots on goal.
Notes: Washington defenceman Mike Green was back on the ice after missing 10 games with a groin injury.